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Analysis of left-truncated right-censored or doubly censored data with linear transformation models

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Abstract

We analyze left-truncated right-censored (LTRC) data or doubly censored data using semiparametric transformation models. It is demonstrated that the extended estimating equations of both Cheng et al. (Biometrika 82:835–845, 1995) and Chen et al. (Biometrika 89:659–668, 2002) can be used to analyze LTRC data or doubly censored data when left-censored variables are always observed. The asymptotic properties of the proposed estimators are derived. A simulation study is conducted to investigate the performance of the proposed estimators.

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References

  • Bennett S (1983) Analysis of survival data by the proportional odds model. Stat Med 2:273–277

    Article  Google Scholar 

  • Cai T, Cheng SC (2004) Semiparametric regression analysis for doubly censored data. Biometrika 91:277–290

    Article  MathSciNet  MATH  Google Scholar 

  • Chang MN (1990) Weak convergence of a self-consistent estimator for the survival function with doubly censored data. Ann Stat 18:391–404

    Article  MATH  Google Scholar 

  • Chang MN, Yang GL (1987) Strong consistency of a nonparametric estimator of the survival function with doubly censored data. Ann Stat 15:1536–1547

    Article  MathSciNet  MATH  Google Scholar 

  • Chen K, Jin Z, Ying Z (2002) Semiparametric analysis of transformation models with censored data. Biometrika 89:659–668

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng SC, Wei LJ, Ying Z (1995) Analysis of transformation models with censored data. Biometrika 82(4):835–845

    Article  MathSciNet  MATH  Google Scholar 

  • Cox D (1972) Regression models and life tables (with Discussion). J R Stat Soc B 34:187–220

    MATH  Google Scholar 

  • The CSHA working group (1994) Canadian study of health and aging: study methods and prevalence of dementia. J Can Med Assoc 150:899–913

    Google Scholar 

  • Gu MG, Zhang CH (1993) Asymptotic properties of self-consistent estimators based on doubly censored data. Ann Stat 21:611–624

    Article  MathSciNet  MATH  Google Scholar 

  • Gross ST, Lai TL (1996) Bootstrap methods for truncated censored data. Stat Sin 6:509–530

    MathSciNet  MATH  Google Scholar 

  • Iglesias-Pérez CJ, González-Manteiga WG (1999) Strong representation of a generalized product-limit estimator for truncated and censored data with some application. J Nonparametr Stat 10:213–244

    Article  MATH  Google Scholar 

  • Lai TL, Ying Z (1991) Estimating a distribution function with truncated and censored data. Ann Stat 19:417–422

    Article  MathSciNet  MATH  Google Scholar 

  • Leiderman PH, Babu D, Kagia J, Kraemer HC, Leiderman GF (1973) African infant precocity and some social influences during the first year. Nature 242:247–249

    Article  Google Scholar 

  • Liang KY, Zeger SL (1986) Longitudinal data analysis using generalized linear models. Biometrika 73:13–22

    Article  MathSciNet  MATH  Google Scholar 

  • Murphy SA, Rossini AJ, van der Vaart AW (1996) Maximum likelihood estimation in the proportional odds model. J Am Stat Assoc 92:968–976

    Article  Google Scholar 

  • Mandel M (2007) Censoring and Truncation—Highlighting the Differences. Am Stat 61:321–324

    Article  MathSciNet  Google Scholar 

  • Mykland PA, Ren J (1996) Algorithms for computing self-consistent and maximum likelihood estimators with doubly censored data. Ann Stat 24:1740–1764

    Article  MathSciNet  MATH  Google Scholar 

  • Pan W, Chappell R (2002) Estimation in the Cox proportional hazards model with left-truncated and interval-censored data. Biometrics 58:64–70

    Article  MathSciNet  MATH  Google Scholar 

  • Pollard D (1990) Empirical processes: theory and applications. Institute of Mathematical Statistics, Hayward

    MATH  Google Scholar 

  • Ren J (1997) On self-consistent estimators and kernel density estimators with doubly censored data. J Stat Plan Inference 64:27–43

    Article  MATH  Google Scholar 

  • Shen P-S (2003) The product-limit estimate as an inverse-probability-weighted average. Commun Stat, Theory Methods 32(6):1119–1133

    Article  MATH  Google Scholar 

  • Shen P-S (2009) An inverse-probability-weighted approach to the estimation of distribution function with doubly censored data. Stat Probab Lett 79:1269–1276

    Article  MATH  Google Scholar 

  • Shen P-S (2010, accepted), Generalized time-dependent conditional linear model with Left-truncated and right-censored data. Commun Stat Theory Methods

  • Shen P-S (2011) Semiparametric analysis of transformation models with doubly censored data. J Appl Stat 38:675–682

    Article  MathSciNet  Google Scholar 

  • Tsai WY, Crowley J (1985) A large sample study of generalized maximum likelihood estimators from incomplete data via self-consistency. Ann Stat 13:1317–1334

    Article  MathSciNet  MATH  Google Scholar 

  • Tsai W-Y, Jewell NP, Wang M-C (1987) A note on the product-limit estimate under right censoring and left truncation. Biometrika 74:883–886

    Article  MATH  Google Scholar 

  • Turnbull BW (1974) Nonparametric estimation of a survivorship function with doubly censored data. J Am Stat Assoc 69:169–173

    Article  MathSciNet  MATH  Google Scholar 

  • Turnbull BW (1976) The empirical distribution with arbitrarily grouped, censored and truncated data. J R Stat Soc B 38:290–295

    MathSciNet  MATH  Google Scholar 

  • Wang M-C (1987) Product-limit estimates: a generalized maximum likelihood study. Commun Stat, Theory Methods 6:3117–3132

    Google Scholar 

  • Wang M-C (1991) Nonparametric estimation from cross-sectional survival data. J Am Stat Assoc 86:130–143

    Article  MATH  Google Scholar 

  • Yang S, Prentice R (1999) Semiparametric inference in the proportional odds regression model. J Am Stat Assoc 92:968–976

    MathSciNet  Google Scholar 

  • Zeng D, Lin DY (2007) Maximum likelihood estimation in semiparametric regression model with censored data. J R Stat Soc B 69:507–564

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Tunghai University, Taichung, 40704, Taiwan

    Pao-sheng Shen

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  1. Pao-sheng Shen
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Correspondence to Pao-sheng Shen.

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Shen, Ps. Analysis of left-truncated right-censored or doubly censored data with linear transformation models. TEST 21, 584–603 (2012). https://doi.org/10.1007/s11749-011-0263-1

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  • DOI: https://doi.org/10.1007/s11749-011-0263-1

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